Condensed Matter Theory

Abstract:

We study the spin quantum Hall effect and transitions between Hall plateaus in quasi two-dimensional network models consisting of several coupled layers. Systems exhibiting the spin quantum Hall effect belong to class C in the symmetry classification for Anderson localisation, and for network models in this class there is an established mapping between the quantum problem and a classical one involving random walks. This mapping permits numerical studies of plateau transitions in much larger samples than for other symmetry classes, and we use it to examine localisation in systems consisting of $n$ weakly coupled layers. Standard scaling ideas lead one to expect $n$ distinct plateau transitions, but in the case of the unitary symmetry class this conclusion has been questioned. Focussing on a two-layer model, we demonstrate that there are two separate plateau transitions, with the same critical properties as in a single-layer model, even for very weak interlayer coupling.

Abstract:

We investigate the phase diagram of bosons interacting via Feshbach-resonant pairing interactions in a one-dimensional lattice. Using large scale density matrix renormalization group and field theory techniques we explore the atomic and molecular correlations in this low-dimensional setting. We provide compelling evidence for an Ising deconfinement transition occurring between distinct superfluids and extract the Ising order parameter and correlation length of this unusual superfluid transition. This is supported by results for the entanglement entropy which reveal both the location of the transition and critical Ising degrees of freedom on the phase boundary.